'You know it's ready to harvest when the top stalk has two buds' ... Yemen's Nabil Ali Rafik, 17, shows off his qat plants in Wadi Dahr. Photograph: Hugh Macleod

There's something a bit different about the three Rafik brothers as they show off their fields of lanky green trees, grown from the rich and rare soils of Wadi Dahr.

Unlike three-quarters of Yemeni men on the afternoon of a day off, there are no little green flecks around the teeth of Abdullah, Nabil and Ahmed: they are not chewing qat – they are growing it.

The bitter and mildly narcotic leaf is key to Yemen's economy, and yet its enormous need for water is on course to make the capital, Sana'a, the first in the world to die of thirst. With the problem extending across the nation, the country is almost literally chewing itself to death.

From high on the scorched brown rock face that surrounds the Wadi Dahr valley, half an hour's drive north-west of Sana'a, the fertile carpet of vegetation below looks miraculous. Like most of Yemen, these northern mountains are a dry and barren land. But the irrigation needed to grow qat, coupled with an exploding population, means Sana'a's water basin is emptying out at a staggering rate: four times as much water is taken out of the basin as falls into it each year.

Most experts predict Sana'a, the fastest-growing capital in the world at 7% a year, will run out of economically viable water supplies by 2017. That is the same year the World Bank says Yemen will cease earning income from its oil, which currently accounts for three-quarters of the state's revenues.

The cost of water in some suburbs of Sana'a has tripled in the last year, and armed conflicts over water resources around the city are increasing. Shortages in the summer months leave thousands of families with taps run dry, forcing them to spend a third of their meagre incomes on buying water from trucks.

According to Mahmoud Shidiwah, chair of the Yemeni government's water and environment protection agency, 19 of the country's 21 main water aquifers are no longer being replenished after a long drought and increasing demand. He says Yemen, the poorest country in the Arab world, receives under 200 cubic metres a person a year, well below the international water poverty line of 1,000 cubic metres. The water basin in Taiz, one of Yemen's largest cities, has already collapsed. Neighbouring Amran is close, as is Saada in the north.

The water situation is so serious that the government has considered moving the capital, as well as desalinating seawater on the coast and pumping it 2,000 metres uphill to the capital. A third solution would be to transfer water over the mountains from another basin. Shidiwah says: "We have a very big problem. All options have been found to be unacceptable."

The best solution, everyone agrees, is to reduce qat growing, which sucks up the largest share of water use. But this is also fraught with social and political problems, says Shidiwah, because in a country where half the population earn less than $2 a day it provides many jobs.

A meeting of Yemen's Gulf Arab neighbours this weekend in Riyadh, following a conference in London in January, is expected to make pledges of development assistance to the failing state. However, the UN's appeal for $177m in humanitarian aid this year is so far only 0.4% funded, leading the World Food Programme earlier this month to cut back rations for around 1 million Yemenis. A recent WFP survey found that one out of every three Yemenis – 7.5 million people – suffer chronic hunger.

Once a vibrant farming economy, Yemen today imports up to 80% of its food needs. The residents of Rawda, one of six districts that make up the sprawling suburbs of Sana'a known as Beni al Harith, know why.

"In the 1970s this was all covered with trees. We used to grow the most delicious grapes in the republic. Now they come from outside," says Abdel Latif al Oulofi, a community leader.

"In the 1980s the population was 5,000. Now there are more than 100,000 people. We know of 1,500 illegal wells, most of them now dry. People have been drilling with oil rigs, going down 600 metres to try and find water. But the wells are so polluted we have to rely on trucks. Rawda means paradise. It was very beautiful. Now it's like hell."

A further irony is that Yemen is subsidising its own drought. Officials estimate that a billion litres of diesel were used last year just for pumping water for agriculture. As the government subsidises most of the cost of diesel, the state calculates it spent $700m on depleting its own national water resources.

Oulofi promises to set up a meeting later in the afternoon with Rawda's sheikh, or tribal leader, who will be discussing water issues with local families.

But the view over Wadi Dahr shows why little explanation for Yemen's water woes is needed: the rows and rows of green trees below do not bear fruit and vegetables, but solely the qat leaf.

"You know it's ready to harvest when you see the top stalk has two buds," says the youngest of the three Rafiks, 17-year-old Nabil Ali, as he pulls down the bendy trunk of a hamdani tree, one of Sana'a's most popular qat varieties.

Weaving along the heavily potholed track leading out of Wadi Dahr, and the phone rings. It's Oulofi with bad news. The sheikh has been laid up in the local clinic, put on a drip and told to rest for the next two days. He won't be able to discuss water with his community until at least next week. The reason for the sheikh's sudden collapse? Sunstroke and dehydration.

State of crisis

Saudi Arabia is hosting a meeting on Yemen's most urgent development and financial needs as efforts intensify to boost international support for reforms by President Ali Abdullah Salih. Yemen is often described a state in danger of failing. In addition to its acute water crisis, it is also running out of oil — its main source of revenue — and has to support a rapidly growing and young population with high rates of illiteracy, malnutrition and unemployment. International ­interest was galvanised by the abortive attempt to bomb a US airliner over Detroit on Christmas Day, claimed by the Yemen-based al-Qaida in the ­Arabian Peninsula. Under US pressure, Yemeni authorties have targeted al-Qaida more aggressively.